Shooting groups over 1.2 inches is not surprising if you are outside the preferred velocity for your stock & barrel combination and you are shooting with an OAL that happens to fit outside the harmonic balance of the rifle for that load.

I agree with several posters on your 44 grain 4895 load being on the high end.
I have never had really accurate groups that high up in the velocity range but I admit that I haven't shot more than 42.6 grains of H4895 either. That was where the accuracy started to really go south with that powder in my rifle. The 168 grain bullet groups at that load of H4895 for 4 different bullets at different depths averaged 0.626 with the worst load shooting 1.208 on average.

I noticed that you were using 2.800 as the OAL seating length. Some of my worst groups were shot at 2.800 seating depth, especially with bullets that have the ogive pretty far back from the tip. Then again with a different powder or bullet, some of the best groups were shot at 2.800 and 2.805. Some rifles have deep chambers and prefer a but deeper seating to get good performance.

I have had good results from H4895 in the 41.8 to 42.3 range using Sierral Match King 168 grain bullets depending on the seating depth. When I find a node (at 41.8 grains for example at 2.820 OAL), I find that I can retain the accuracy at that node if I reduce the OAL by 0.0005 for every 12.5 fps that I increase the velocity of a load. I have verified that the same effect holds for 175 grain SMKs and Nosler CC bullets.

I recently tried Nosler Custom Competition 168 grain bullets and have found they like to be seated about 0.01 deeper than the SMKs in my rifle to find the same accuracy node.

I recently have tried Vihta Vuori N140 powder in a range of 41.1 through 42.3 grains and have had even better results than with H4895. Looks like the velocity my rifle likes with N140 is a bit slower but, on average, the accuracy that results is slightly better than for H4895.

My best 10 hand loads with my .308 average 0.471 at 100 yards for 78 groups with 8 different 168 grain loads, one 150 grain load and one 175 grain load.
Six of the 168s are with Nosler bullets and the other 4 are with 150, 168 (2) and 175 SMKs.